Question: Solve for $x$ and $y$ using elimination. ${-x-5y = -14}$ ${x-2y = 7}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-7y = -7$ $\dfrac{-7y}{{-7}} = \dfrac{-7}{{-7}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-x-5y = -14}\thinspace$ to find $x$ ${-x - 5}{(1)}{= -14}$ $-x-5 = -14$ $-x-5{+5} = -14{+5}$ $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ You can also plug ${y = 1}$ into $\thinspace {x-2y = 7}\thinspace$ and get the same answer for $x$ : ${x - 2}{(1)}{= 7}$ ${x = 9}$